In a Fizeau interferometer, two optical flats such as A and B, having surfaces 1 and 2, respectively, face each other and form a cavity 4, as shown in FIG. 1. The interference fringes produced by the interferometer reveal the optical path difference (OPD) between the adjacent surfaces 1 and 2 that define cavity 4. If one of the surfaces, for example, a reference surface, is perfectly flat, the optical path difference at each pixel of CCD camera 22 represents the topography of the other surface, thereby indicating the degree of flatness or non-flatness of that other surface. If the reference surface is not perfectly flat, then the accuracy of testing the flatness of the other surface is limited by the imperfection in the reference surface.
To obtain absolute measurements of flatness of a test surface, various techniques have been described, the most prominent references in this area being G. Schulz, "Ein interferenzverfahren zur absolute ebnheitsprufung langs beliebiger zntralschnitte", Opt. Acta, 14, 375-388 (1967), and G. Schulz and J Schwider, "Interferometric Testing of Smooth Surfaces", Progress in Optics XIII, E. Wolf, ed., Ch. IV (North-Holland, Amsterdam, 1976). These references describe what is referred to as the "traditional three-flat method", in which two pairs of "flats", or objects with flat surfaces are compared in pairs. For example, flats A and B are compared by obtaining interferometric measurements of the cavity between them, and flats A and C similarly are compared using interferometric measurements defining a slightly different cavity between flats A and C, and similarly for the pair of flats B and C. The flats of one of the pairs then are rotated relative to each other and similar interferometric measurements between the flats of that pair again are made. Then computations are made upon the measured data to obtain exact profiles along several diameters of each flat. Since it usually is desirable to have the topography of an entire flat surface, rather than profiles along a few diameters, the basic method described above has been improved upon to obtain profiles along a large number of diameters of each flat of each pair. Several methods, including those described in B. S. Fritz, "Absolute Calibration of an Optical Flat", Opt. Eng. 23, 379-383 (1984 ); J. Grzanna and G. Schulz, "Absolute Testing of Flatness Standards at Square-Grid Points", Opt. Commun. 77, 107-112 (1990); C. Ai, H. Albrecht, and J. C. Wyant, "Absolute Testing of Flats Using Shearing Technique", OSA annual meeting (Boston, 1991); J. Grzanna and G. Schulz, "Absolute Flatness Testing by the Rotation Method with Optimal Measuring Error Compensation", Appl. Opt. 31, 3767-3780 (1992); G. Schulz, "Absolute Flatness Testing by an Extended Rotation Method Using Two Angles of Rotation", Applied Optics, Vol. 32, No. 7 pp. 1055-1059 (1993), and W. Primak, "Optical Flatness Standard II: Reduction of Interferograms", SPIE Proceeding 954, 375-381 (1989), have been proposed to measure the flatness of the entire surface. The latter methods involve tremendous numbers of least squares calculations, which are very time-consuming, and more importantly, they result in loss of resolution of the profiles of the flat surfaces defining the cavities because least squares methods always tend to smooth the data.
Using the prior techniques, the above-mentioned exact profiles along individual diameters of a test flat have been attainable using four measurements of a pair of flats A and B, another pair of flats A and C, and yet another pair of flats B and C. Conventional phase-shifting interferometry using a Fizeau interferometer has been used to obtain the cavity shape, which constitutes the above-mentioned optical path difference for each pixel between adjacent faces of the two flats being compared. An example of the foregoing technique would involve four measurements M.sub.1, M.sub.5, M.sub.6 and M.sub.8, subsequently explained with reference to FIG. 5B. The most that can be achieved from the prior three-flat method for absolute testing of optical flatness is obtaining of absolute profiles of each flat surface along a large number of diameters of each flat.
Manufacturers of conventional interferometers often have proprietary software for performing the foregoing three-flat testing procedures. Although such software usually is made available to the purchasers of the interferometers, the software has no capability of performing absolute testing of entire surfaces of flats in any way that is not limited by the accuracy of the reference flat. No product presently is commercially available that allows a user of commercially available interferometers to achieve full surface absolute testing of optical flats with precision greater than that of the reference flat being used.
Users of equipment to measure absolute flatness of a test surface generally would prefer to make as few interferometric measurements as possible, because of the tedious, time-consuming nature of mounting a plurality of optical flats on the interferometer and precisely rotating them relative to each other with the needed degree of precision. This involves loosening clamps to allow removal and installation of the flats and very careful handling of the flats.
It would be highly desirable to have a fast, economical way of testing the absolute flatness of a surface with accuracy that exceeds that of the reference flat being used.
There is an unmet need for a fast, economical method and apparatus for absolute testing of an entire surface area of an optical flat.